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Relative Extrema
(a) Graph the fourth-degree polynomial for and 3. For what values of the constant a does p have a relative minimum or relative maximum?
(b) Show that p has a relative maximum for all values of the constant a.
(c) Determine analytically the values of a for which p has a relative minimum.
(d) Let be a relative extremum of p. Show that (x, y) lies on the graph of . Verify this result graphically by graphing together with the seven curves from part (a).
Conjecture a formula for finding a polynomial of degree n giventhe numbers P(0)=a0 , p'(0)=a1 .....p^n(0)=an.
Note: in a0,a1,an, the 0,1,and n are subscripts!
the definition from n! may be helpful